Yes, they make custom backpacks for these. They’re big/thick enough that, due to the retractable landing gear, they take up a whole backpack… You’re not going to easily, say, bring a Phantom and overnight camping supplies.
These things are amazingly stable. If you follow the directions (compass calibration, wait for GPS lock, etc.) they just stay where they are until you tell them to move. It’s nothing like the single-rotor helicopters. And they now have auto-takeoff and auto-landing.
Still, I’d suggest practicing with a Hubsan X4 rather than learning with $1,000+ worth of hardware. They’re only $40 and will teach you the controls. And the Hubsan isn’t GPS stabilized (but it’s still way more stable than the single-rotor helicopters), so the Phantom 3 will feel like a breeze afterwards.
The P3 does come with a simulator, if you’re using an iOS device. You just connect it to your controller and you can fly the sim on your iPhone or iPad. (The Android app doesn’t yet have the sim.) When I got my Phantom 1 last year, I actually taught myself using the free trial version of Heli-X (which has a Phantom 1 in GPS-disabled mode) with an Xbox controller. But now that the Hubsan is so cheap, I’d go that route instead.